Nuclear magnetic resonance imaging (MRI) apparatuses are diagnostic imaging apparatuses for medical use that induce nuclear magnetic resonance in nuclei of hydrogen atoms contained in any plane traversing a subject, and that produce a tomographic image of a region contained in the plane using generated nuclear magnetic resonance signals. In general, when slice-selective magnetic field gradients are applied in order to identify a plane of a subject whose tomographic image is to be produced, excitation pulses are applied in order to excite magnetizations in the plane at the same time. Nuclear magnetic resonance signals (echoes) are produced in the course of the precession of the excited magnetizations. In order to given positional information to the magnetizations, phase-encoding magnetic field gradients and readout magnetic field gradients which are perpendicular to each other in a section are applied during a period from excitation to acquisition of the echoes. The measured echoes are mapped to a k-space having an axis of abscissas kx and an axis of ordinates ky, and inverse Fourier transform is performed in order to reconstruct an image.
The pulse and magnetic field gradients to be used to generate an echo are applied according to a predefined pulse sequence. As for the pulse sequence, various pulse sequences are known in association with different purposes. For example, a gradient echo (GrE) type high-speed imaging method is a method in which: the pulse sequence is repeatedly implemented; and the phase-encoding magnetic field gradient is sequentially changed with every repetition in order to sequentially measure the number of echoes required for producing one tomographic image.
FIG. 1 shows a pulse sequence employed in a gradient echo type hybrid radial scanning method that is one of radial scanning methods. FIG. 2 shows the map of measured echoes in the k-space. Herein, four blocks are defined in the k-space.
Actions to be performed in order to implement a pulse sequence 701 will be described below. Namely, slice-selective magnetic field gradient pulses 701-1 to 701-4 oriented in a z direction are applied, and dephasing magnetic field gradient pulses 702-1 to 702-4 and magnetization exciting radiofrequency magnetic field pulses (RF pulses) 700-1 to 700-4 whose frequency corresponds to the resonant frequency f0 of protons are applied in order to induce a nuclear magnetic resonance phenomenon in protons contained in a slice of an object concerned. After dephasing magnetic field gradient pulses 705-1 to 705-4 and 706-1 to 706-4 are applied, while readout magnetic field gradient pulses 703-1 to 703-4 and 704-1 to 704-4 are applied, nuclear magnetic resonance signals (echoes) 707-1 to 707-4 are measured. The pulse sequence 701 is composed of four parts 708-1, 708-2, 708-3, and 708-4, each of which is repeated Cr times while the magnitudes of the dephasing magnetic field gradient pulses 705-1 to 705-4 and 706-1 to 706-4 are varied. The echoes 707-1, 707-2, 707-3, and 707-4 measured with the respective parts are mapped to blocks 1, 2, 3, and 4 that are equidistantly defined in a θ direction as shown in FIG. 2. The positions of the echoes in the blocks are determined with the magnitudes of the pulses 705-1 to 705-4 and 706-1 to 706-4.
The k-space is converted into a Cartesian grid using a gridding technique (refer to, for example, non-patent document 1). Thereafter, two-dimensional inverse Fourier transform is performed in order to reconstruct an image. An imaging time per image is a product of the time (repetition time TR) from the beginning of the part 708-1 to the end of the part 708-1 and the number of echoes. For example, when TR equals 4 ms and 128 echoes are used to reconstruct one image, the imaging time comes to 512 ms.
According to the imaging method, data in the central region of the k-space equivalent to a low-spatial frequency portion of an image is repeatedly acquired as shown in FIG. 2. The center of the k-space shall be referred to as a reference domain 222. A method in which the reference domain 222 is used to compensate rotations and translations out of the motions of the subject rendered by the blocks has been proposed (refer to, for example, non-patent document 2). According to the method, after a magnitude of rotation is detected and compensated, a magnitude of translation is detected and compensated.
In rotation detection, since the rotation of an image space leads to the rotation of absolute values in the k-space, correlation is performed in the k-space. Gridding is performed on each of the blocks within the reference domain in the k-space, and a mean of each block within the reference domain is regarded as criterial data. While the reference-domain data of each block is rotated, gridding is performed in order to obtain an angle maximizing the value of the correlation to the criterial data.
As for a magnitude of translation, a mean of reference-domain data of each of the blocks having undergone gridding after the completion of rotation compensation is adopted as criterial data. A product of the criterial data by the reference-domain data of each of the blocks is Fourier-transformed. The position indicated by the peak among the resultant data sets is used to detect the magnitude of translation.
As for filling of the k-space with data, according to an enhanced reconstruction method using periodically rotated overlapping parallel lines, data of a bundle of echoes (blade) acquired after every excitation is subjected to two-dimensional Fourier transform and then to positional correction (refer to, for example, non-patent document 3).
Non-patent document 1: “Selection of a Convolution Function for Fourier Inversion Using Gridding” by Jackson JI, Meyer CH, Nishimura DG (IEEE Trans. Med. Imaging, Vol. 10, No. 3, pp. 473-478, 1991)
Non-patent document 2: “Motion Correction With PROPELLER MRI: Application to Head Motion and Free-breathing Cardiac Imaging” by J. G. Pipe (Magn. Reson. Med., pp. 963-969, 1999)
Non-patent document 3: “Effect on Motion Correction of an Echo Train Length and the Number of Blades set for PROPELLER MRI (Computer Simulation)” (Journal of Japan Radiological Society, Vol. 60, No. 2, pp. 264-269)